Excerpt from Math Odyssey 2000

The story of Emmy Noether raises the questions of "nature or nurture"? Did she become a great mathematician by heredity? (after-all, her father was a very high ranking mathematician) or by environment? (he exerted a very strong influence over his children and created a "mathematical atmosphere" in his household). She certainly had the right genes, and she later proved to be a true mathematical genius; but as a very young child, Emmy had exhibited absolutely no interest in mathematics. When her younger brother, Fritz, began to fall under the influence of her father, she eventually had to take up the subject, possibly, in an effort to defend herself in a household of mathematicians. Lynn Osen, one of her biographers writes:

*"If the ambience of her home had been different, she might have never
chosen a career in mathematics, but the provocative discussions that swooped
and soared around the young Emmy's head sparked an interest that was overpowering."*

Lynn M. Osen, Women In Mathematics , MIT Press, Cambridge, 1974

At age 18, she entered the University of Erlangen, where her father was a mathematics professor; she completed her undergraduate work and then received her doctorate in mathematics at age 25. During the years immediately after her graduation, her father began suffering from a long term illness, and Emmy would teach his classes at the university for him. She was also asked to give an occasional lecture on her research, but she did not have a permanent position on the faculty. At this time (around 1907), her most productive research was in the field of abstract algebra, and she often visited Gottingen where David Hilbert was working in the same field. Hilbert recognized her genius and persuaded her to move to Gottingen to join with him and Felix Klein in their work on the general theory of relativity. Between 1908 and 1915, she was regularly presenting papers at math society meetings and was soon invited by Hilbert to teach at the university in Gottingen.

As was true with all other female mathematicians, Emmy had to overcome a considerable number of obstacles in order to gain her well-deserved recognition. Women were not actually allowed to be on the faculty at this university, so she would teach classes under Hilbert's name. (The class schedule would show that the course was being taught by David Hilbert, but everyone, including the students, knew that Emmy was teaching it.) In 1919 she was given the rank of "unofficial" associate professor, a title that carried no salary and no duties, although she did teach.

In the 1920's her research activity developed the field of abstract algebra to its highest levels. Her research output was phenomenal and she exerted a great influence over many young mathematicians. The Soviet Encyclopedia of Mathematics devotes more than seven pages to her works (and one page to the works of her father). While it's true that counting pages is certainly not a foolproof way to measure mathematical greatness, it does tend to give some indication of the breadth, and permanence of a mathematician's creations. Very few other mathematicians come any where close to matching the significance of her work, no matter how you measure it. In his book, Men of Mathematics , Eric Temple Bell describes her as " the most creative abstract algebraist in the world." Many of the mathematical topics that she invented were later developed by other mathematicians into important results. For example, she determined an axiom system for various algebraic systems including the general theory of ideals and, apparently, she contributed a significant part of Van der Waerden's book Modern Algebra.

Gottingen in the 1920's and early 1930's was considered to be the foremost university in the world for the study of mathematics, and it is clear that Emmy Noether made major contributions to its success. In 1933, with the rise of Adolf Hitler and his oppressive regime in Germany, Emmy fled Gottingen and ended up as a professor of mathematics at Bryn Mawr University. At last, she was given the recognition due a great mathematician; she continued her research and teaching at Bryn Mawr and with some of her former colleagues at the Institute for Advanced Study in Princeton. She died in 1935.

Here is a quote of what Albert Einstein said of her after her death: In the judgment of the most competent living mathematicians, Fraulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began. In the realm of algebra in which the most gifted mathematicians have been busy for centuries, she discovered methods which have proved of enormous importance in the development of the present day younger generation of mathematicians.

**EXERCISES **

- Which do think is more important in the development of a mathematician, heredity or environment? Which of these applies best to Emmy Noether?
- Who was the famous mathematician that invited Emmy to teach at the University of Gottingen, and what were the unusual circumstances associated with her teaching assignment?
- How would you rank Emmy Noether among female mathematicians? How would you rank her among all mathematicians?

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